Time Travel and Its Paradoxes
Time travel is a staple of fiction, but it is also a serious probe of the metaphysics of time: asking whether, and how, travel to the past could be coherent forces every commitment about tense, the existence of times, persistence, and causation into the open. And it is not merely idle: general relativity permits spacetimes with closed timelike curves — worldlines that loop back to their own past — so the question "is past-directed time travel possible?" is partly a question about the solutions of the field equations, not only about what we can imagine. The philosophical payoff is the grandfather paradox and its relatives, which turn out to show not that time travel is impossible but that it is subject to a stringent and illuminating consistency constraint.
This page distinguishes the paradoxes, states the Lewisian resolution, and connects to the physics of closed timelike curves.
What "time travel" would be
David Lewis's classic analysis ("The Paradoxes of Time Travel," 1976) begins by defining the phenomenon. A time traveller is someone for whom the duration of the journey, measured by the traveller's own personal time (their biological processes, their watch, their memories), differs from the interval of external time between departure and arrival. Step into the machine, experience an hour pass, and step out a century earlier: one hour of personal time, minus one century of external time. Personal time is what orders the stages of the traveller in the four-dimensionalist sense; external time is the B-series of the world. Genuine (past-directed) time travel requires the two to come radically apart — and, crucially, that the traveller's worldline be continuous in personal time while looping in external time.
The grandfather paradox
The famous puzzle: you travel to the past and kill your grandfather before he sires your parent. Then you are never born; then you never travel back to kill him; then he lives and you are born — and so on, contradiction. Doesn't this show past-directed time travel is impossible?
Lewis's answer is no — the paradox shows only that time travel, if it occurs, must be globally self-consistent. The reasoning:
- There is exactly one past, and it either does or does not contain your grandfather's early death. The past is not "changed" by time travel — the very idea of changing the past is incoherent, because it would require the past to be one way (grandfather survives) and then another way (grandfather dies), which needs a second time dimension along which the change occurs. There is no such hyper-time. The traveller does not change the past; the traveller was always already a part of the past they visit.
- So can you kill your grandfather? In the ordinary sense — you have a gun, the skill, the opportunity — yes: relative to the facts about your abilities and surroundings, you "can." But relative to the further fact that your grandfather demonstrably survived to have descendants (you are here), you will not succeed: something will stop you — the gun jams, you lose your nerve, you shoot the wrong man, you miss. Not because a mysterious force protects the timeline, but simply because the past is already a certain way, and only self-consistent sequences of events actually happen. The "can" and "cannot" are compossibility relative to different sets of facts, equivocating on which the paradox trades.
The upshot is the consistency constraint (the "Novikov self-consistency principle" in the physics literature): the only histories that occur are those that are globally consistent — no genuine contradiction is ever realised. Time travel is possible; changing the past is not; and the appearance of paradox comes from illicitly imagining the past as alterable.
Causal loops and the bilking argument
A subtler difficulty is the causal loop (or "bootstrap" paradox): information or objects that come from nowhere. A time traveller gives Beethoven the scores of the symphonies she memorised — which he then "composes," which are printed, which she later memorises and carries back. Who wrote them? Each event has a cause within the loop, but the loop as a whole has no external origin; the information exists uncreated. Such loops are not contradictions (unlike a realised grandfather paradox), so the consistency constraint permits them, but many find them objectionably "unexplained" — the loop is causally closed and its contents seem to spring from nothing.
Related is the bilking argument against backward causation generally: if an effect precedes its cause , then in the interval one could observe whether has occurred and then deliberately prevent — "bilking" the cause — which appears to refute the backward-causal claim. Defenders reply that the very setup, if backward causation is real, must be self-consistent: the bilking attempt is itself part of the history and, like grandfather-murder, will systematically fail to break the loop. The bilking argument thus reduces to the same consistency constraint rather than to an outright impossibility.
Closed timelike curves in general relativity
The philosophy is not free-floating, because general relativity contains solutions with closed timelike curves (CTCs) — worldlines everywhere future-directed that nonetheless return to their starting event, so that an observer following one would, without ever "going backward," arrive in their own past:
- Gödel's rotating universe (1949): a cosmological solution, sourced by rotating dust with a suitable cosmological constant, in which CTCs pass through every event. Gödel drew an explicitly philosophical moral: if time can loop, then time does not "pass" in any objective, global sense, and the A-theory of an advancing worldwide present is untenable — a striking argument for the B-theory from pure general relativity.
- Other CTC spacetimes: the interior of rotating (Kerr) black holes, Tipler cylinders, and traversable-wormhole models all admit CTCs.
Whether such solutions are physically realisable is disputed. Gödel's universe does not match our (non-rotating, expanding) cosmos; wormhole CTCs may require exotic negative-energy matter. Hawking's chronology protection conjecture proposes that quantum effects (diverging vacuum fluctuations as a CTC forms) always intervene to prevent CTCs from actually developing — "making the universe safe for historians" — but this remains a conjecture pending a full theory of quantum gravity.
What time travel presupposes
The coherence of time travel has morals for the metaphysics of time:
- It fits most comfortably with the B-theory and eternalism: a fixed, tenselessly existing block universe in which the traveller's whole looping worldline simply is, consistently, part of the four-dimensional whole. Gödel's argument makes this explicit.
- It sits awkwardly with presentism: if only the present exists, "travelling to the past" is travelling to something that does not exist — presentists must work hard to make sense of a destination that is unreal.
- It requires the perdurantist picture to be stated cleanly: the traveller is a spacetime worm whose personal-time ordering of stages loops back through external time, so that two stages of one person can be simultaneous (the young and old versions meeting).
Where this sits
Time travel is the stress test of the temporal question: it shows that the real constraint is global consistency, not the fictional "changing the past," and it turns the abstract choice between A- and B-theories, presentism and eternalism, and endurance and perdurance into a concrete verdict, generally favouring the tenseless block universe. It is also where the metaphysics of time meets general relativity most dramatically, through closed timelike curves, and where a final answer waits on quantum gravity and the fate of chronology protection. This completes the time subfolder; the space pages take up the third master question — the structure and epistemology of geometry.